The iterative solver template library. The numerical solution of partial differential equations frequently requires the solution of large and sparse linear systems. Using generic programming techniques in C++ one can create solver libraries that allow efficient realization of “fine grained interfaces”, i.e. with functions consisting only of a few lines, like access to individual matrix entries. This prevents code replication and allows programmers to work more efficiently. We present the “Iterative Solver Template Library” (ISTL) which is part of the “Distributed and Unified Numerics Environment” (DUNE). It applies generic programming in C++ to the domain of iterative solvers of linear systems stemming from finite element discretizations. Those discretizations exhibit a lot of structure. Our matrix and vector interface supports a block recursive structure. Each sparse matrix entry can itself be either a sparse or a small dense matrix. Based on this interface we present efficient solvers that use the recursive block structure via template metaprogramming.

References in zbMATH (referenced in 15 articles )

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  1. Gratien, Jean-Marc: A robust and scalable multi-level domain decomposition preconditioner for multi-core architecture with large number of cores (2020)
  2. Vidotto, Ettore; Koch, Timo; Köppl, Tobias; Helmig, Rainer; Wohlmuth, Barbara: Hybrid models for simulating blood flow in microvascular networks (2019)
  3. Kröner, Axel; Kröner, Eva; Kröner, Heiko: Finite element approximation of level set motion by powers of the mean curvature (2018)
  4. Schmidt, Stephan: Weak and strong form shape hessians and their automatic generation (2018)
  5. Hunt, Alexander; Surulescu, Christina: A multiscale modeling approach to glioma invasion with therapy (2017)
  6. Schneider, Martin; Agélas, Léo; Enchéry, Guillaume; Flemisch, Bernd: Convergence of nonlinear finite volume schemes for heterogeneous anisotropic diffusion on general meshes (2017)
  7. Schneider, Martin; Gläser, Dennis; Flemisch, Bernd; Helmig, Rainer: Nonlinear finite-volume scheme for complex flow processes on corner-point grids (2017)
  8. Mitchell, Lawrence; Müller, Eike Hermann: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling (2016)
  9. Tobias Leibner, Rene Milk, Felix Schindler: Extending DUNE: The dune-xt modules (2016) arXiv
  10. Efendiev, Yalchin; Kronsbein, Cornelia; Legoll, Frédéric: Multilevel Monte Carlo approaches for numerical homogenization (2015)
  11. Bastian, Peter; Heimann, Felix; Marnach, Sven: Generic implementation of finite element methods in the distributed and unified numerics environment (DUNE) (2010)
  12. Dedner, Andreas; Klöfkorn, Robert; Nolte, Martin; Ohlberger, Mario: A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module (2010)
  13. Gräser, Carsten; Sander, Oliver: The DUNE-subgrid module and some applications (2009)
  14. Bastian, P.; Blatt, M.; Dedner, A.; Engwer, C.; Klöfkorn, R.; Kornhuber, R.; Ohlberger, M.; Sander, O.: A generic grid interface for parallel and adaptive scientific computing. II: Implementation and tests in DUNE (2008)
  15. Scheichl, R.; Vainikko, E.: Additive Schwarz with aggregation-based coarsening for elliptic problems with highly variable coefficients (2007)